27:
43:
224:". Example/theory: A hole (usually 6–10 inches in diameter) is dug in the ground surface (usually 12–24" deep). Water is filled in to the hole, and the time is measured for a drop of one inch in the water surface. If the water surface quickly drops, as usually seen in poorly-graded sands, then it is a potentially good place for a septic "
142:
is needed beforehand to determine whether the intended structure is likely to succeed or fail. In two dimensional square lattice percolation is defined as follows. A site is "occupied" with probability p or "empty" (in which case its edges are removed) with probability 1 – p; the corresponding
86:. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.
181:
Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used. The current fastest algorithm for percolation was published in 2000 by
195:
Coffee percolation (see Fig. 1), where the solvent is water, the permeable substance is the coffee grounds, and the soluble constituents are the chemical compounds that give coffee its color, taste, and
537:
Lee, Lye Siang; Brunk, Nicholas; Haywood, Daniel G.; Keifer, David; Pierson, Elizabeth; Kondylis, Panagiotis; Wang, Joseph Che-Yen; Jacobson, Stephen C.; Jarrold, Martin F.; Zlotnick, Adam (2017).
99:
743:
713:
705:
147:
205:
Collapse and robustness of biological virus shells to random subunit removal (experimentally-verified fragmentation of viruses).
217:
Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus
789:
284:
228:". If the hydraulic conductivity of the site is low (usually in clayey and loamy soils), then the site is undesirable.
309:
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812:
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102:, has brought new understanding and techniques to a broad range of topics in physics, materials science,
324:
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348:; Ziff, Robert (2000). "Efficient Monte Carlo Algorithm and High-Precision Results for Percolation".
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114:, percolation refers to filtration of water through soil and permeable rocks. The water flows to
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20:
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Brunk, Nicholas E.; Lee, Lye Siang; Glazier, James A.; Butske, William; Zlotnick, Adam (2018).
785:
739:
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589:(1983). "On the Critical Behavior of the General Epidemic Process and Dynamical Percolation".
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In coffee percolation, soluble compounds leave the coffee grounds and join the water to form
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539:"A molecular breadboard: Removal and replacement of subunits in a hepatitis B virus capsid"
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482:"Molecular jenga: The percolation phase transition (collapse) in virus capsids"
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Cracking of trees with the presence of two conditions, sunlight and pressure.
439:
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572:
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466:
423:"Percolation Theory Reveals Biophysical Properties of Virus-like Particles"
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Movement of weathered material down on a slope under the earth's surface.
42:
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127:
111:
51:
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31:
616:
Newman, M. E. J. (2002). "Spread of epidemic disease on networks".
41:
25:
78: 'to filter, trickle through') refers to the movement and
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are planned to dispose of substantial amounts of water, a
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34:. Insoluble compounds (and granulates) remain within the
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of fluids through porous materials. It is described by
19:
For the mathematical and statistical physics term, see
738:, Taylor & Francis, 1994, revised second edition,
220:
Potential sites for septic systems are tested by the "
433:(8). American Chemical Society (ACS): 12988–12995.
421:Brunk, Nicholas E.; Twarock, Reidun (2021-07-23).
170:are used to characterize percolation properties.
143:problem is called site percolation, see Fig. 2.
16:Filtration of fluids through porous materials
8:
762:Remarkable properties of pawns on a hexboard
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784:, Cambridge University Press, 2006,
110:, and other fields. For example, in
736:Introduction to Percolation Theory
698:Applications of Percolation Theory
14:
154:concepts such as scaling theory,
46:Percolation in a square lattice.
146:Percolation typically exhibits
700:, Taylor & Francis, 1994.
285:Percolation critical exponents
174:is commonly employed to study
1:
751:"Percolation and Conduction"
603:10.1016/0025-5564(82)90036-0
98:, the mathematical study of
392:10.1103/PhysRevLett.85.4104
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648:10.1103/PhysRevE.66.016128
310:Self-organized criticality
208:Transport in porous media.
18:
755:Reviews of Modern Physics
94:During the last decades,
591:Mathematical Biosciences
506:10.1088/1478-3975/aac194
440:10.1021/acsnano.1c01882
351:Physical Review Letters
734:; and Aharony, Ammon;
728:Springer Verlag, 1999.
685:"What is percolation?"
176:percolation thresholds
72:
47:
39:
325:Water pipe percolator
295:Percolation threshold
45:
29:
795:Grimmett, Geoffrey;
760:Rodrigues, Edouard;
749:Kirkpatrick, Scott;
725:Percolation (2. ed).
270:Groundwater recharge
640:2002PhRvE..66a6128N
498:2018PhBio..15e6005B
374:2000PhRvL..85.4104N
214:Surface roughening.
211:Spread of diseases.
152:Statistical physics
136:septic drain fields
132:infiltration basins
767:2021-12-09 at the
732:Stauffer, Dietrich
720:Grimmett, Geoffrey
696:Sahimi, Muhammad;
690:Notices of the AMS
624:(1 Pt 2): 016128.
587:Grassberger, Peter
290:Percolation theory
250:Critical exponents
164:critical phenomena
130:. In places where
96:percolation theory
48:
40:
21:percolation theory
618:Physical Review E
549:(11): 2170–2180.
358:(19): 4104–4107.
320:Supercooled water
305:Self-organization
186:and Robert Ziff.
60:materials science
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799:, Springer, 1999
757:, 45, 574, 1973.
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104:complex networks
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681:Kesten, Harry
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275:Immunization
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148:universality
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108:epidemiology
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797:Percolation
782:Percolation
693:, May 2006.
315:Septic tank
245:Conductance
226:leach field
184:Mark Newman
124:water table
120:groundwater
100:percolation
84:Darcy's law
64:percolation
807:Categories
790:0521872324
332:References
90:Background
66:(from
708:(cloth),
449:1936-0851
378:CiteSeerX
222:perc test
80:filtering
74:percolare
56:chemistry
765:Archived
716:(paper).
664:15291065
656:12241447
573:28795465
524:29714713
467:34296852
427:ACS Nano
400:11056635
260:Gelation
233:See also
190:Examples
168:fractals
128:aquifers
116:recharge
636:Bibcode
564:5654856
515:6004236
494:Bibcode
458:8397427
370:Bibcode
122:in the
112:geology
52:physics
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196:aroma.
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32:coffee
753:, in
687:, in
660:S2CID
626:arXiv
404:S2CID
360:arXiv
70:
68:Latin
786:ISBN
740:ISBN
710:ISBN
702:ISBN
652:PMID
569:PMID
520:PMID
463:PMID
445:ISSN
396:PMID
166:and
126:and
118:the
644:doi
599:doi
559:PMC
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510:PMC
502:doi
453:PMC
435:doi
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